Incentivizing Agents through Ratings

I study the optimal design of performance or product ratings to motivate agents' performance or investment in product quality. The principal designs a rating that maps their quality (performance) to possibly stochastic scores. Agents have private information about their abilities (cost of effort/quality) and choose their quality. The market observes the scores and offers a wage equal to the agent's expected quality [resp. ability]. I first show that an incentive-compatible interim wage function can be induced by a rating (i.e., feasible) if and only if it is a mean-preserving spread of quality [resp. ability]. Thus, I reduce the principal's rating design problem to the design of a feasible interim wage. When restricted to deterministic ratings, the optimal rating design is equivalent to the optimal delegation with participation constraints (Amador and Bagwell, 2022). Using optimal control theory, I provide necessary and sufficient conditions under which lower censorship, and particularly a simple pass/fail test, are optimal within deterministic ratings. In particular, when the principal elicits maximal effort (quality), lower censorship [resp. pass/fail] is optimal if the density is unimodal [resp. increasing]. I also solve for the optimal deterministic ratings beyond lower censorship for general distributions and preferences. For general ratings, I provide sufficient conditions under which lower censorship remains optimal. In the effort-maximizing case, a pass/fail test remains optimal if the density is increasing.